Localization in nets of standard spaces

Lechner, Gandalf ORCID: https://orcid.org/0000-0002-8829-3121 and Longo, Roberto 2015. Localization in nets of standard spaces. Communications in Mathematical Physics 336 , pp. 27-61. 10.1007/s00220-014-2199-2

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Abstract

Starting from a real standard subspace of a Hilbert space and a representation of the translation group with natural properties, we construct and analyze for each endomorphism of this pair a local, translationally covariant net of standard subspaces, on the lightray and on two-dimensional Minkowski space. These nets share many features with low-dimensional quantum field theory, described by corresponding nets of von Neumann algebras. Generalizing a result of Longo and Witten to two dimensions and massive multiplicity free representations, we characterize these endomorphisms in terms of specific analytic functions. Such a characterization then allows us to analyze the corresponding nets of standard spaces, and in particular to compute their minimal localization length. The analogies and differences to the von Neumann algebraic situation are discussed.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Mathematics
Subjects:	Q Science > QA Mathematics
Publisher:	Springer Verlag
ISSN:	0010-3616
Date of First Compliant Deposit:	30 March 2016
Date of Acceptance:	5 May 2014
Last Modified:	18 Nov 2024 00:30
URI:	https://orca.cardiff.ac.uk/id/eprint/73586

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